Question: Ben is 2 times as old as Daniel. 21 years ago, Ben was 9 times as old as Daniel. How old is Daniel now?
Answer: We can use the given information to write down two equations that describe the ages of Ben and Daniel. Let Ben's current age be $b$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $b = 2d$ 21 years ago, Ben was $b - 21$ years old, and Daniel was $d - 21$ years old. The information in the second sentence can be expressed in the following equation: $b - 21 = 9(d - 21)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = 2d$ . Substituting this into our second equation, we get: $2d$ $-$ $21 = 9(d - 21)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $2 d - 21 = 9 d - 189$ Solving for $d$ , we get: $7 d = 168.$ $d = 24$.